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Correct OPTION is (C) 45

The best I can explain: The LOSS tangent is tan δ, where δ is the loss angle. Given that loss tangent tan δ = 1. Thus we get δ = tan^-1(1) = 450.

Right option is (a) σ/ωε

To elaborate: The CONDUCTION current DENSITY is Jc = σ E and the displacement current density is Jd = jωεE. Its magnitude will be ωεE. Thus the LOSS TANGENT TAN δ = Jc /Jd = σ/ωε is the required expression.

Right OPTION is (b) TAN 40

The BEST explanation: The angle of the loss tangent δ is twice the intrinsic angle θn. THUS tan δ = tan 2θn = tan 2(20) = tan 40.

The correct choice is (c) DISSIPATION factor

For explanation: The loss tangent is the measure of the loss of POWER due to PROPAGATION in a DIELECTRIC, when compared to that in a conductor. HENCE it is also referred to as dissipation factor.

Right answer is (b) Displacement current

The best I can explain: The conduction current OCCURS in METALS and is INDEPENDENT of the frequency. The attenuation and PHASE constant highly depend on the varying frequency. The displacement current occurs due to dielectrics and is significant only at very high FREQUENCIES.

Correct choice is (c) 5/4.5

For explanation I would say: The conduction current density is the PRODUCT of the CONDUCTIVITY and the electric FIELD. The resistivity is the reciprocal of the conductivity. Thus the required FORMULA is Jc = σ E = E/ρ = 5/4.5 units.

Right answer is (c) Flemming rule

To ELABORATE: By Flemming’s rule, when the thumb and the middle finger represent the inputs (SAY current and field respectively), then the fore finger represents the output (FORCE, in this CASE). The EM PROPAGATION can be illustrated by this rule.

Right ANSWER is (a) Power DUE to propagation in conductor to that in dielectric

To elaborate: The loss tangent is the tangent angle formed by the plot of conduction CURRENT density vs displacement current density. It is the RATIO of Jc by Jd. It represents the loss of power due to propagation in a dielectric, when compared to that in a conductor.

Right option is (c) 8

Explanation: The TIME constant of CAPACITOR is given by T = RC, where R = 4×10^6 and C = 2×10^-6. THUS T = 4×10^6 x2x10^-6 = 8 seconds.

Right answer is (a) –με dV/dt

To explain: The GRADIENT of A is the RATIO of the NEGATIVE gradient of electric potential to the speed of LIGHT C. We can write c = 1/√(με). Thus grad(A) = -με dV/dt is the required expression.

Right option is (d) –dA/dt

To explain: The electric field intensity is GIVEN by E = -GRAD(V)- dA/dt, where V is the electric POTENTIAL and A is the MAGNETIC VECTOR potential. When V is zero, then E = -dA/dt.

The correct choice is (a) True

To explain: Fields that varying sinusoidally with respect to TIME are called as HARMONIC fields. An EXAMPLE for harmonic fields is A sin wt.

Right option is (c) B

For EXPLANATION I would say: The DIVERGENCE of the magnetic flux density is ALWAYS ZERO. By Stokes theorem, the surface integral of B is same as the volume integral of the divergence of B. Thus the surface integral of B is also zero.

Right ANSWER is (b) DISPLACEMENT current density

The best EXPLANATION: The capacitor consists of a dielectric placed between TWO conducting PLATES, subjected to a field. The current due to a dielectric is always due to the displacement current density.

Correct choice is (B) 1.732

Explanation: From the Ampere circuital law, the curl of H is the conduction current density. The curl of H = yi + ZJ + xk is –i – J – k. Thus conduction current density is –i – j – k. The magnitude will be √(1 + 1 + 1) = √3 = 1.732 units.

The CORRECT choice is (b) -15

Best explanation: From Maxwell first law, we GET Curl of E as the NEGATIVE DERIVATIVE of B with respect to time. Thus Curl(E) = -dB/dt. On substituting B= 15t and differentiating, Curl(E) = -15 units.

The CORRECT option is (a) E

To explain: The field is irrotational for static fields. Thus curl of E is zero. From Stokes theorem, the LINE integral of E is same as the surface integral of the curl of E. SINCE it is zero, the line integral of E will also be zero.

Correct answer is (b) Irrotational

The EXPLANATION: For STATIC fields, the charges will be constant and the field is constant. Thus curl of the electric field intensity will be zero. This IMPLIES the field is irrotational.

The CORRECT option is (C) EMF = ∫ E.dl

The best I can explain: The emf induced in a material is given by the line INTEGRAL of the ELECTRIC field INTENSITY. Thus EMF = ∫ E.dl is the correct relation.

The correct answer is (d) 3/2.5

The best I can EXPLAIN: The electric field intensity is the electric force per unit charge. It is given by E = F/Q. On substituting F = 2.5 and q = 3, we get E = 3/2.5 units.

Right choice is (b) -180

For explanation: The EMF induced is the product of the turns and the flux rate. Thus Vemf = -Ndφ/dt. On substituting N = 60 and dφ/dt = 3, we GET emf as -60 X 3 = -180 UNITS.

The CORRECT option is (C) -14

Easiest EXPLANATION: The emf induced in a material with flux linkage is GIVEN by Vemf= -dλ/dt. On substituting λ= 3.5t^2, we get emf = -7t. At TIME t = 2sec, the emf will be -14 units.

Correct CHOICE is (B) No

The best explanation: When dielectric breakdown occurs, the MATERIAL LOSES its dielectric property and becomes a CONDUCTOR. When it is subjected to a magnetic field, north and south flux lines coexists, giving magnetic force. Thus there exists magnetic dipole. Suppose if the conductor is broken into very small pieces, still there exist a magnetic dipole in every broken part. In other words, when a piece is broken into half, there cannot exist a north pole in one half and a south pole in the other. Thus monopoles never exist.

The correct answer is (d) Surface INTEGRAL of B is zero

For explanation I WOULD say: We know that the divergence of B is zero. From Stokes THEOREM, the surface integral of B is equal to the volume integral of divergence of B. THUS surface integral of B is ALSO zero.

Correct choice is (b) Divergence

To explain: The Maxwell fourth law or the Gauss law for magnetic field states that the divergence of B is zero, implies the NON EXISTENCE of magnetic MONOPOLES. THUS the operation involved is divergence.

Right answer is (a) The magnetic FIELD cannot be SPLIT

Easy explanation: Practically monopoles do not exist, due to the connection between north and south poles. But theoretically, they exist. The REASON for their non- existence practically is that, the magnetic field CONFINED to two poles cannot be split or confined to a single pole.

Correct OPTION is (a) E-B-H

The explanation: From E, we can COMPUTE B using the MAXWELL first LAW. Using B, the parameter H can be found since B = μH. Thus the sequence is E-B-H is true.

Correct answer is (a) E-D-H-B

Best explanation: From E, D can be COMPUTED as D = εE. Using the Ampere LAW, H can be computed from D. Finally, B can be CALCULATED from H by B = μH.

The correct option is (d) All cases

Easy EXPLANATION: The Gauss law for magnetic field STATES that the divergence of B is always ZERO. This is valid for all cases like free space, dielectric MEDIUM etc.

Right option is (b) Div(H) = 0

Easy EXPLANATION: From the Gauss law for magnetic field, the DIVERGENCE of the magnetic flux density is zero. Also B = μH. THUS divergence of H is also zero, i.e, Div(H) = 0 is true.

Right ANSWER is (d) Magnetic FLUX density

To explain I would say: The divergence of the magnetic flux density is zero. This is the Maxwell fourth EQUATION. As the divergence is zero, the quantity will be solenoidal or DIVERGENT LESS.

Correct option is (d) 3

Explanation: The DIVERGENCE of the electric flux density is the charge density. For a POSITION vector xi + YJ + zk, the divergence will be 1 + 1 + 1 = 3. Thus by Gauss law, the charge density is also 3.

The correct OPTION is (C) E

Easy explanation: From the Gauss law for electric field, we can find the electric FLUX DENSITY directly. On substituting, D= ε E, the electric field intensity can be CALCULATED.

The correct choice is (c) 6

Easiest explanation: By Gauss LAW, Div(D) = ρv. To GET D, integrate the charge DENSITY given. Thus D = ∫ρv dv, where ρv = 12 and ∫dv = 0.5. We get, D = 12 x 0.5 = 6 units.

Correct choice is (b) 0

The best I can explain: The Gauss THEOREM for an electric field is given by Div(D)= ρ. In a dipole only static CHARGE exists and the divergence will be ZERO. Thus the Gauss theorem VALUE for the dipole will be zero.

Correct answer is (d) Divergent

To EXPLAIN: In any medium other than the air, the conduction is possible, due to the CHARGE carriers. Thus charge density is also non-zero. We can write from Gauss law that Div(D) is non-zero. When the divergence is said to be non-zero, the field is not SOLENOIDAL or CALLED as divergent field.

Correct option is (B) 0

Easy explanation: In free space or AIR, the charge DENSITY will be zero. In other words, the CONDUCTION is POSSIBLE in mere air medium. By gauss law, since the charge density is same as the divergence of D, the Div(D) in air/free space will be zero.

Right option is (d) Divergence of D

The explanation is: From the GAUSS law for electric field, the volume CHARGE DENSITY is the divergence of the electric FLUX density of the field. Thus Div(D) = ρv.

Correct answer is (b) 0.5i + j -1.5k

Explanation: By Maxwell SECOND EQUATION, the curl of H is same as the sum of conduction CURRENT density and DISPLACEMENT current density. Thus Curl(H) = J = 0.5i + j – 1.5k units.

The CORRECT choice is (a) Jd = jwεE

For explanation I would say: The displacement CURRENT density is Jd = dD/dt. Since D = εE and in frequency DOMAIN d/dt = JW, thus we get Jd = jwεE.

Right answer is (C) STOKES THEOREM

Explanation: To convert line integral to surface integral, i.e, in this CASE from line integral of H to surface integral of J, we use the Stokes theorem. Thus the Maxwell second equation can be written as ∫H.dl = ∫∫J.ds.